You need to install and wire the equipment according to the labeling and instructions. I'm not harshing on your asking a question, but note that that the following (and thus the reading) is a Code requirement.
There is already a harness of control wires running between the outdoor and indoor unit(s). The interior unit powers nothing but a fan and some LEDs, so most mini-split installations simply throw fan power into that bundle. Thus it is powered from the outdoor unit.
20A receptacles on 30A breakers
That's a no-go. The receptacle size must match the breaker size exactly for 20A, 30A and 50A breakers. 15A receptacles on 20A circuits are an exception, not a rule.
It's perfectly fine to use larger wire than is required, so the #10 is all good.
Further, the mini-split instructions are probably going to require a dedicated circuit. And are probably going to require it be hard-wired.
A disconnect near the A/C.
Code requires a disconnect switch near the unit - as in line-of-sight near, not "other side of wall" near.
Instructions will also (most likely) specify a hard-wired connection with a disconnect.
Now, 'ratchet freak' suggesed a subpanel to split the 30A into dual 20A circuits (or 20A and 15A depending on the needs of the MrCool). I totally agree. Note that a subpanel qualifies as a disconnect, so if the subpanel is placed outside near the unit, and feeds the compressor outlet back inside, we just crossed off the disconnect requirement :) "That was easy"
A 120V outlet is required within 25' of the unit
That is so the maintainer can plug in their vacuum pump. It is NOT required to be dedicated for the mini-split, it can be a general-use outlet. Yes, I know the MrCool unit is DIY for initial installation, but it might need servicing later by a pro certified for handling refrigerants. It's not just the certification, it's the required recovery equipment to prevent damage to the atmosphere, and the supply chain to recycle or destroy that refrigerant.
You cannot get 120V from a 240V circuit that you ran with /2 cable. (however if you ran /3 cable and you take it to a subpanel, you can stick a 120V breaker in the subpanel). Feel free to Extend some other shop circuit if needed.